Magnetically Coupled System For Mixing

ABSTRACT

The invention provides a mixing system comprising a magnetically coupled drive system and a foil for cultivating algae, or cyanobacteria, in an open or enclosed vessel. The invention provides effective mixing, low energy usage, low capital expenditure, and ease of drive system component maintenance while maintaining the integrity of a sealed mixing vessel.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. application Ser. No.13/405,012, filed Feb. 24, 2012; U.S. Provisional Patent Application No.61/575,644, filed Aug. 24, 2011; and U.S. Provisional Patent ApplicationNo. 61/447,004, filed Feb. 25, 2011, the disclosures of each of whichare incorporated herein by reference. This application incorporatesGroup III claims from parent U.S. application Ser. No. 13/405,012, whichgroup of claims was defined in a requirement for restriction that issuedin the parent application and which claims were not elected forexamination in the parent application. A utility patent applicationtitled “Magnetically Coupled System For Mixing” is being filed by thesame applicant for this application on the same date of the filing ofthis application and incorporates Group I claims from parent U.S.application Ser. No. 13/405,012, which group of claims was defined inthe requirement for restriction issued in the parent application andwhich claims were not elected for examination in the parent application.This application and the utility patent application titled “MagneticallyCoupled System For Mixing” being filed by the same applicant for thisapplication on the same date of the filing of this application aredivisional applications.

BACKGROUND

The present invention relates generally to mixing systems for use inenclosed vessels, such as rigid or flexible enclosures, or open vessels,such as pond systems, which may serve as reactors, bioreactors orphotobioreactors. Systems in accordance with the present invention maybe used to cultivate algae and other microorganisms in water forpurposes such as producing biofuels, bulk chemicals, pharmaceuticalcompounds or other products or treating wastewater.

High density, high pigment aqueous algae cultures require mixing toevenly distribute nutrients to microorganisms in the culture and toensure that the microorganisms in the culture are cyclically exposed tolight needed for photosynthesis. One of the key challenges forcommercial-scale mixing systems is to minimize the use of energy andcapital expense while providing optimal production conditions.

Large, open pond systems typically use large paddle wheel mixers to movewater around a raceway, but paddle wheel mixers are inefficient andrequire significant energy inputs, which may be cost-prohibitive for usein cultivation of microorganisms for the production of biofuel or othercommodities. In addition, paddle wheel mixers are designed to move waterin a path of horizontal flow and do not effectively move algae in avertical plane, which is needed to ensure even exposure of the algae tolight at the surface of the aqueous culture.

In “Biotechnology of Algal Biomass Production: A Review of Systems forOutdoor Mass Culture,” Journal of Applied Phycology 5: 593-604 (1993),Chaumont reviews mixing techniques proposed for use with algae cultures,including forcing culture through a slit in a board dragged through anopen pond; “a mixing system consisting of a continuous flume containingarrays of foils similar in design to segments of airplane wings”;airlift; injectors; propellers; pump and gravity flow devices usingnatural energy sources; open pond loop “raceways” incorporatingpaddlewheel stirring devices; and sloped ponds and other cultivationunits having parallel troughs or baffles, for example.

In “Photobioreactors for Mass Cultivation of Algae,” BioresourceTechnology 99: 4021-4028 (2008). Ugwu et al. note that inefficientstirring mechanisms in open cultivation systems yield poor mass transferrates that result in low biomass productivity.

Vertical photobioreactor systems use pumps, blowers or compressed air tointroduce rising air bubbles and produce turbulent fluid motion in theaqueous algal culture for the purpose of mixing. Horizontalphotobioreactor systems typically use pumps to circulate the culture andcreate turbulence in the aqueous algae culture to provide mixing.

Ugwu et al. (“Photobioreactors for Mass Cultivation of Algae”) describethe use of air-pump, bubble column and airlift systems to mix culturesin tubular and vertical-column photobioreactors.

The effects and performance of mixing in vessels such as bioreactorshave also been investigated for numerous configurations of other mixingelements, such as the combination of radial impellers with axialup-pumping hydrofoils (Vrabel et al., “Mixing in Large-Scale VesselsStirred With Multiple Radial or Radial and Axial Up-Pumping Impellers:Modelling and Measurements,” Chemical Engineering Science, Vol. 55, No.23: 5881-5896 (2000)); a rotating impeller in combination with glasstubes acting as baffle plates (Ogbanna et al., “A Novel InternallyIlluminated Stirred Tank Photobioreactor for Large-Scale Cultivation ofPhotosynthetic Cells,” Journal of Fermentation and Bioengineering, Vol.82, No, 1: 61-67 (1996)); up-pumping impellers (Nienow et al., TheVersatility of Up-Pumping Hydrofoil Agitators,” Chemical EngineeringResearch and Design, Vol. 82, No. 9: 1073-1081 (2004)); axial and mixeddual-impeller systems (Bouaifi et al., “Power Consumption, Mixing Timeand Homogenisation Energy in Dual-Impeller Agitated Gas-LiquidReactors,” Chemical Engineering and Processing, Vol. 40, No, 2: 87-95(2001)); the combination of airlift with hydrofoil impellers (Chisti etal., Oxygen Transfer and Mixing in Mechanically Agitated AirliftBioreactors.” Biochemical Engineering Journal, Vol. 10, No, 2: 143-153(2002)); and turbines, down-pumping hydrofoils and up-pumping hydrofoils(Boon et al., “Comparing a Range of Impellers for ‘Stirring as FoamDisruption’,” Biochemical Engineering Journal, Vol. 10, No. 3: 183-195(2002)).

In “A Simple Algal Production System Designed to Utilize the FlashingLight Effect,” Biotechnology and Bioengineering, Vol. XXV: 2319-2335(1983) and in “High Algal Production Rates Achieved in a Shallow OutdoorFlume,” Biotechnology and Bioengineering, Vol. XXVIII: 191-197 (1986),Laws et al. describe gains in solar energy conversion efficiency andalgae production yielded by emplacing arrays of foils similar in designto airplane wings to create vortices and systematic mixing in an algalculture flume.

Many of these methods provide mixing regimes for high-density algaecultures but consume too much energy to be cost effective in theproduction of biofuel, bulk chemicals or other commodities on anindustrial scale. The required energy inputs for such methods andconfigurations exceed the energy yield that can be produced by the algaeculture in the form of, for example, biofuel. Accordingly, a need existsfor a mixing system that provides sufficient mixing and gas transfer foroptimal production of biofuel and other materials while maintainingacceptable energy consumption in the context of operating costs for thereactor system and minimizing capital expense.

In addition, a need exists to provide effective mixing and gas transferin vessels such as bioreactors and photobioreactors while maintainingstructural integrity of the vessel, minimizing risk of contamination ofthe contents of the vessel, minimizing exposure of pumps and othermixing drive system components to corrosive agents in the vessel andfacilitating ease of maintaining the drive system components. Variousmixing apparatuses rely on the use of rotary impellers and similarelements that are not physically connected to a drive motor but insteadare driven by magnetic coupling.

U.S. Pat. No. 7,824,904 (Dimanshteyn for “Photobioreactors forProduction of Algae and Methods Therefor”) discloses mixing a liquidmicrobial culture using a rotary or oscillatory system comprising one ormore motors, one or more shafts connected to the one or more motors anda plurality of mixing blades attached to the one or more shafts.

U.S. Pat. Appl. Pub. No. 2009/0035856 (Galliher et al. for “ContinuousPerfusion Bioreactor System”) discloses vessels such as a disposable,collapsible bag having an integrated magnetically-driven rotatingimpeller that provides mixing for cell culture, cell containment,bioreactor and/or pharmaceutical manufacturing systems.

U.S. Pat. Appl. Pub. No. 2009/0130757 (Terentiev for “Bioreactor WithMixer and Sparger”) discloses a bioreactor that comprises an impellerpositioned within an interior compartment of the vessel that is rotatedby way of a magnetic coupling.

U.S. Pat. Appl. Pub. No. 2011/0003366 (Zeikus for “Methods of UsingPneumatic Bioreactors”) discloses a pneumatic bioreactor containing afluid to be mixed that includes a floating impeller that rises in thefluid as gas bubbles carry it upward to the surface and falls when thegas is then vented, wherein the mixing speed is controlled withelectromagnets in the vessel acting upon magnetic material in theimpeller or its guides.

PCT Published Patent Application WO 2005/121310 (Johnson et al. for“Creation of Shear in a Reactor”) discloses the use of a applying amagnetic field to a magnetically-activated element to generate shear ina liquid sample.

U.S. Pat. Appl. Pub. No. 2009/0219780 (Castillo et al. for “MixingSystem Including a Flexible Bag, Specific Flexible Bag and LocatingSystem for the Mixing System”) discloses a mixing system comprising aflexible bag with a rotary magnetic impeller and an alignmentfacilitation device adapted to facilitate alignment between the magneticimpeller and a magnetic driver located external to the system.

In “Design, Construction and Testing of Pilot Scale PhotobioreactorSubsystems,” Master of Science (MS) Thesis, Ohio University, MechanicalEngineering (Engineering and Technology), 2008, Mears describes the workof Tsygankov (2001) involving a coaxial cylinder reactor in which twocoaxial tubes are placed one inside the other with algae fluid locatedin the annular space between the surfaces of both tubes. Mears furtherdescribes the reactor of Tsygankov incorporating a ferromagnetic ring inthe section containing the algae and applying a magnetic field to movethe ring back and forth, mixing the algae liquid.

In “Microbioreactors for Bioprocess Development,” Journal of theAssociation for Laboratory Automation, Vol. 12, No. 3: 143-151 (2007),Zhang et al. describe the use of a magnetic stir bar to mix a microbialsolution in a cylindrical reactor chamber.

A need exists to incorporate a magnetic coupling drive system with amixing configuration that is effective in a photobioreactor whilemaintaining the structural integrity of the photobioreactor and abilityto service the components of the drive system without compromising thealgae culture therein.

The above discussion includes both information known to the art prior tothe filing date and information forming part of the present inventivedisclosure. Inclusion of any statement in this section, whether as acharacterization of a published reference or in a discussion oftechnical problems and their solutions, is not to be taken as anadmission that such statement is prior art.

SUMMARY OF INVENTION

An object of this invention is a magnetically coupled mixing systemadapted to provide vertical mixing in an open or enclosed vessel whileadvantageously maintaining low energy usage requirements.

A further object of this invention is a magnetically coupled mixingsystem adapted to provide gas transfer in an open or enclosed vesselwhile advantageously maintaining low energy usage requirements.

A further object of this invention is a magnetically coupled mixingsystem wherein components used to drive the mixing system are locatedoutside a sealed mixing vessel, permitting access outside the sealedmixing vessel for greater ease of maintaining the drive components,while maintaining the integrity of the sealed mixing vessel.

Accordingly, this invention provides for a magnetically coupled mixingsystem comprising a mixing vessel; a liquid mixture disposed within thereactor vessel; a drive conduit; a drive element disposed within thedrive conduit and adapted to move in a longitudinal direction within thedrive conduit; a follower member having a first distal end and a seconddistal end, wherein the follower member is disposed around the perimeterof the drive conduit and is adapted to move longitudinally along thedrive conduit; a magnetic follower element disposed within the followermember, wherein the magnetic follower element is adapted to couplemagnetically with the drive element and is proximally disposed outsidethe drive conduit; a foil having a surface shaped or configured toprovide hydrodynamic lift, wherein the foil is disposed at leastpartially in the liquid mixture; and a support member connecting thefoil and the follower member.

This invention also provides for a magnetically coupled mixing systemcomprising a mixing vessel; a liquid disposed within the mixing vessel;a gas disposed within the mixing vessel; a drive conduit; a driveelement disposed within the drive conduit and adapted to move in alongitudinal direction within the drive conduit; a follower memberhaving a first distal end and a second distal end, wherein the followermember is disposed around the perimeter of at least a portion of thedrive conduit and is adapted to move longitudinally along the driveconduit; a magnetic follower element disposed within the followermember, wherein the magnetic follower element is adapted to couplemagnetically with the drive element and is proximally disposed outsidethe drive conduit; and a crossbar attached to the follower member,wherein the crossbar is at least partially disposed in the liquid, thecrossbar mixes the liquid, the gas, or an interface between the liquidand the gas, the crossbar has a surface shaped or configured to generatea breaking wave front in the liquid, and the breaking wave front isgenerated by movement of the crossbar along a linear path in the mixingvessel.

This invention also provides for a magnetically coupled mixing systemcomprising drive fluid contained within the drive conduit and a pump incommunication with the drive conduit, wherein the pump is adapted tomove the drive fluid and the drive element within the drive conduit.

This invention also provides for a magnetically coupled mixing systemwherein the drive fluid is air, water, mineral oil or polyethyleneglycol.

This invention also provides for a magnetically coupled mixing systemwherein the drive fluid contains corrosion-inhibiting agents.

This invention also provides for a magnetically coupled mixing systemwherein the pump is a reversible flow pump.

This invention also provides for a magnetically coupled mixing systemwherein the pump is a positive displacement pump or a velocity pump.

This invention also provides for a magnetically coupled mixing systemwherein the pump is a diaphragm pump or a centrifugal pump.

This invention also provides for a magnetically coupled mixing systemcomprising a flow control valve.

This invention also provides for a magnetically coupled mixing systemwherein the pump is located outside of the mixing vessel.

This invention also provides for a magnetically coupled mixing systemwherein the mixing vessel is an enclosed vessel, an open vessel, areactor, a bioreactor, a photobioreactor or an open pond. In the contextof a photobioreactor comprising cells in a liquid suspension, themagnetic mixing system of the present invention employing a linearlymoving foil provides gentle vertical mixing which allows for particledistribution and movement within a light field but without damagingcells. For situations wherein the cells are producing a target molecule,the cost of the energy consumed by the mixing system of the presentinvention is less than the value of the target molecule, with energyconsumed and molecules produced averaged over the same time period. In apreferred embodiment, the energy cost is 10% or less of the value of thetarget molecules produced.

This invention also provides for a magnetically coupled mixing systemwherein the liquid mixture comprises algae and water. This inventionalso provides for a magnetically coupled mixing system that may be usedin other commercial processes that require low energy input and regular,gentle mixing in elongate reactors, including but not limited topharmaceutical cell culture, food processing and waste water treatment.This invention also provides for a magnetically driven skimmer that caneconomically remove surface solids that accumulate in algal ponds andwaste water. This invention also provides for a magnetically driven foilthat may be used in a vapor phase to increase the efficiency of a solarstill.

This invention also provides for a magnetically coupled mixing systemwherein the drive conduit is disposed inside the reactor vessel.

This invention also provides for a magnetically coupled mixing systemwherein the drive conduit is disposed at least partially within theliquid mixture.

This invention also provides for a magnetically coupled mixing systemwherein the drive conduit is disposed outside the reactor vessel.

This invention also provides for a magnetically coupled mixing systemcomprising a blocking element disposed within the drive conduit, whereinthe blocking element is adapted to restrict the movement of the driveelement within a desired range within the drive conduit.

This invention also provides for a magnetically coupled mixing systemcomprising a longitudinal vane disposed on an inner surface of the driveconduit such that channels adapted to permit flow of the drive fluid areformed on the inner surface of the drive conduit, wherein the channelsare bounded by the surface of the drive element, the surface of thelongitudinal vane and the inner surface of the elongate tubular hollowmember.

This invention also provides for a magnetically coupled mixing systemcomprising a longitudinal groove formed in an inner surface of the driveconduit such that a channel adapted to permit flow of the drive fluid isformed in the inner surface of the drive conduit, wherein the channelare bounded by the surface of the drive element and the surfaces of thegroove formed in the inner surface of the drive conduit.

This invention also provides for a magnetically coupled mixing systemwherein the drive element is ferromagnetic or magnetic.

This invention also provides for a magnetically coupled mixing systemcomprising materials that suppress corrosion or wear, wherein thematerials coat the drive element.

This invention also provides for a magnetically coupled mixing systemwherein the drive element is spherical or cylindrical.

This invention also provides for a magnetically coupled mixing systemwherein the follower member comprises a hollow elongate tubularenclosure.

This invention also provides for a magnetically coupled mixing systemwherein the magnetic follower element is adapted to move longitudinallywithin the follower member.

This invention also provides for a magnetically coupled mixing systemcomprising a flotation member and a support member connecting theflotation member with the follower member or the foil.

This invention also provides for a magnetically coupled mixing systemwherein the flotation member is configured to provide surface mixing ofthe liquid mixture.

This invention also provides for a magnetically coupled mixing systemwherein the flotation member comprises a pontoon.

This invention also provides for a magnetically coupled mixing systemcomprising a tracking member, wherein the tracking member is proximal toa wall of the mixing vessel and is adapted to prevent the foil and theflotation member from contacting the wall, wherein the support memberconnects the foil, the follower member and the tracking member.

This invention also provides for a magnetically coupled mixing systemcomprising a carrier member in which the magnetic follower element iscontained, wherein the carrier member is proximally disposed outside thedrive conduit.

This invention also provides for a magnetically coupled mixing systemcomprising a bumper element disposed within the follower member.

This invention also provides for a magnetically coupled mixing systemcomprising a flexible elongate tension member that connects the foil orsupport member to the follower member.

This invention also provides for a magnetically coupled mixing systemwherein the foil is uncambered, has a quadrangular planform shape and isconfigured at an angle of attack sufficient to generate hydrodynamiclift and trailing vortices.

This invention also provides for a magnetically coupled mixing systemwherein the foil comprises a cambered surface.

This invention also provides for a magnetically coupled mixing systemwherein the foil is substantially vertically oriented and has a surfaceconfigured and angled to provide hydrodynamic lift.

This invention also provides for a magnetically coupled mixing systemcomprising an axle attached to a support member, wherein the foil isrotatably mounted on the axle.

This invention also provides for a magnetically coupled mixing systemwherein the foil further comprises a weight or a cavity embedded in thefoil proximal to a trailing edge of the foil.

This invention also provides for a magnetically coupled mixing systemwherein the foil further comprises a steering element disposed on thesurface of the foil proximal to a trailing edge of the foil.

This invention also provides for a magnetically coupled mixing systemwherein the planform shape of the foil is bilaterally symmetric and istriangular or quadrangular.

This invention also provides for a magnetically coupled mixing systemcomprising a support member that is substantially horizontally oriented,wherein a top edge of the support member is cambered and is adapted toinduce a hydraulic jump in the liquid mixture.

This invention also provides for a magnetically coupled mixing systemcomprising mixing structures attached to a horizontal support member,wherein the mixing structures are configured to stir the surface of theliquid mixture.

This invention also provides for a magnetically coupled mixing systemcomprising a flexible dredging member attached to the foil, the pontoonor a support member, wherein the flexible dredging member is at leastpartially suspended in the liquid mixture and is configured to inducevertical mixing of the liquid mixture.

This invention also provides for a magnetically coupled mixing systemwherein the foil is pivotally attached to a support member, such thatthe angle of attack of the foil is variable and selectively adjustable.

This invention also provides for a magnetically coupled mixing systemcomprising a poppet valve disposed inside the drive element.

This invention also provides for a magnetically coupled mixing systemcomprising a bypass conduit connected to the drive conduit.

This invention also provides for a magnetically coupled mixing systemcomprising a foil disposed only in gas.

This invention also provides for a magnetically coupled mixing systemcomprising a gas sparging hose attached to the follower member, thefollower element, the foil or the support member.

This invention also provides for a magnetically coupled mixing systemcomprising a Venturi tube formed in the support member, with one openingof the Venturi tube disposed above the surface of the liquid and theopposite opening of the Venturi tube disposed below the surface of theliquid.

This invention also provides for a magnetically coupled mixing systemcomprising a vertically-oriented foil attached to ahorizontally-oriented foil.

This invention also provides for a magnetically coupled mixing systemwherein the mixing system mixes only a portion of the depth of theliquid disposed within the mixing vessel.

This invention also provides for a magnetically coupled mixing systemwherein the mixing system mixes only a portion of the length of theliquid disposed within the mixing vessel.

This invention also provides for a magnetically coupled mixing systemcomprising a mixing vessel; a liquid disposed within the mixing vessel;a foil having a surface shaped or configured to provide hydrodynamiclift, wherein the foil is disposed at least partially in the liquid, andwherein vertical mixing of the liquid is achieved by linear motion ofthe foil in the mixing vessel; a cable attached to the foil; and areversible motor adapted to pull the cable.

This invention also provides for a magnetically coupled mixing systemcomprising a drive conduit; a follower member having a first distal endand a second distal end, wherein the follower member is disposed aroundthe perimeter of at least a portion of the drive conduit and is adaptedto move longitudinally along the drive conduit, and wherein the cable isattached to the foil or the follower member; and a support memberconnecting the foil and the follower member.

This invention also provides for a system for achieving vertical mixingwithin a liquid in a reactor comprising a foil moving by magnetic meansin a linear direction.

This invention also provides for a method to achieve vertical mixing ina liquid in a reactor comprising the steps of moving a drive element ina linear direction within the reactor; magnetically coupling a followerelement to the drive element; and coupling a foil to the followerelement, such that the foil produces vertical mixing in the liquid inthe reactor.

This invention also provides for a system for the production of a targetmolecule or accumulation of biomass comprising a suspension of cells ina liquid, wherein the cells are capable of producing a target moleculeor accumulating biomass; and a foil moving by magnetic means in a lineardirection in the liquid and producing vertical mixing of the suspension;wherein production of the target molecule or accumulation of biomass isgreater in the presence of the moving foil than in the absence of themoving foil; and wherein the system is a bioreactor.

This invention also provides for a system for the production of a targetmolecule or accumulation of biomass comprising a suspension of cells ina liquid, wherein the cells are capable of producing a target moleculeor accumulating biomass; and a foil moving by magnetic means in a lineardirection in the liquid and producing vertical mixing of the suspension;wherein accumulation of biomass is greater in the presence of the movingfoil than in the absence of the moving foil; and wherein the system is abioreactor.

This invention also provides for a system for achieving vertical mixingwithin a fluid in a reactor comprising a foil moving by magnetic meansin a linear direction.

This invention also provides for a method to achieve vertical mixing ina fluid in a reactor comprising the steps of moving a drive element in alinear direction within the reactor; magnetically coupling a followerelement to the drive element; and coupling a foil to the followerelement, such that the foil produces vertical mixing in the fluid in thereactor.

This invention also provides for a magnetically coupled mixing systemcomprising a mixing vessel; a fluid disposed within the mixing vessel; adrive conduit; a drive element disposed within the drive conduit andadapted to move in a longitudinal direction within the drive conduit; afollower member having a first distal end and a second distal end,wherein the follower member is disposed around the perimeter of at leasta portion of the drive conduit and is adapted to move longitudinallyalong the drive conduit; a magnetic follower element disposed within thefollower member, wherein the magnetic follower element is adapted tocouple magnetically with the drive element and is proximally disposedoutside the drive conduit; a foil having a surface shaped or configuredto provide lift, wherein the foil is disposed at least partially in thefluid, and wherein vertical mixing of the fluid is achieved by linearmotion of the foil in the mixing vessel; and a support member connectingthe foil and the follower member.

This invention also provides for a magnetically coupled mixing systemcomprising a mixing vessel; a fluid disposed within the mixing vessel; afoil having a surface shaped or configured to provide lift, wherein thefoil is disposed at least partially in the fluid, and wherein verticalmixing of the fluid is achieved by linear motion of the foil in themixing vessel; a cable attached to the foil; and a reversible motoradapted to pull the cable.

This invention also provides for a magnetically coupled mixing systemcomprising a mixing vessel; a liquid disposed within the mixing vessel;a drive conduit; a drive element disposed within the drive conduit andadapted to move in a longitudinal direction within the drive conduit;and a magnetic follower element disposed around the perimeter of atleast a portion of the drive conduit and adapted to move longitudinallyalong the drive conduit, wherein the magnetic follower element isadapted to couple magnetically with the drive element and is proximallydisposed outside the drive conduit.

This invention also provides for a system for the production of a targetmolecule or accumulation of biomass comprising a suspension of cells ina liquid, wherein the cells are capable of producing a target moleculeor accumulating biomass; and a foil moving by magnetic means in a lineardirection in the liquid and producing vertical mixing of the suspension;wherein the total cost of mixing per unit weight of the target moleculeor biomass produced is lower using the foil to induce vertical mixingthan using a paddlewheel mixer.

BRIEF DESCRIPTION OF DRAWINGS

These and other features, aspects and advantages of this invention willbecome better understood with regard to the following description,appended claims and accompanying drawings where:

FIG. 1 shows a sectional view of a portion of a mixing system inaccordance with certain embodiments of the present invention;

FIG. 2 shows an axial view of a portion of a mixing system in accordancewith certain embodiments of the present invention;

FIG. 3 shows a perspective view of a portion of a mixing system inaccordance with certain embodiments of the present invention;

FIG. 4 shows a perspective view of a portion of a mixing system inaccordance with certain embodiments of the present invention;

FIGS. 5A and B show a perspective and sectional view, respectively, of afollower element in accordance with certain embodiments of the presentinvention;

FIG. 6 shows a sectional view of a portion of a mixing system inaccordance with certain embodiments of the present invention;

FIGS. 7A-H show sectional views of exemplary suitable configurations ofdrive elements and follower elements;

FIG. 8 shows a sectional view of a drive element in accordance withcertain embodiments of the present invention;

FIG. 9 shows a perspective view of a drive element in accordance withcertain embodiments of the present invention;

FIGS. 10A-C show sectional views of a drive element in accordance withcertain embodiments of the present invention;

FIGS. 11A-C show sectional and perspective views of a drive element inaccordance with certain embodiments of the present invention:

FIGS. 12A-D show sectional and perspective views of a drive element inaccordance with certain embodiments of the present invention;

FIG. 13 shows a portion of a mixing system in accordance with certainembodiments of the present invention;

FIG. 14 shows a sectional perspective view of a mixing system andidealized fluid flow in accordance with certain embodiments of thepresent invention;

FIG. 15 shows a sectional perspective view of a mixing system inaccordance with certain embodiments of the present invention;

FIG. 16 shows a sectional perspective view of a mixing system inaccordance with certain embodiments of the present invention;

FIGS. 17A-C show side and front views of portions of mixing systems inaccordance with certain embodiments of the present invention;

FIG. 18 shows a sectional perspective view of an embodiment of a driveconduit;

FIGS. 19A and B show sectional views of a drive element in accordancewith certain embodiments of the present invention;

FIGS. 20A and B show sectional and end views of a drive element inaccordance with certain embodiments of the present invention;

FIGS. 21A and B show sectional and end views of a follower member andbypass conduit in accordance with certain embodiments of the presentinvention;

FIG. 22 shows an embodiment of a hydraulic mixing system in accordancewith certain embodiments of the present invention;

FIG. 23 shows an embodiment of a pneumatic mixing system in accordancewith certain embodiments of the present invention;

FIG. 24 shows a planform schematic view of a mixing system in accordancewith certain embodiments of the present invention;

FIG. 25 shows a planform schematic view of a mixing system in accordancewith certain embodiments of the present invention;

FIG. 26 shows a cable driven mixing system in accordance with certainembodiments of the present invention;

FIG. 27 shows a cable driven mixing system in accordance with certainembodiments of the present invention;

FIG. 28 shows an embodiment of a foil in accordance with certainembodiments of the present invention;

FIG. 29 shows trailing vortices and vertical mixing generated byhorizontal movement of a foil in a mixing system in accordance withcertain embodiments of the present invention;

FIG. 30 shows a computational simulation of trailing vortices andvertical mixing generated by horizontal movement of a foil in a mixingsystem in accordance with certain embodiments of the present invention;

FIG. 31 shows a foil and a flotation member in accordance with certainembodiments of the present invention;

FIGS. 32A and B show foils in accordance with certain embodiments of thepresent invention;

FIGS. 33A and B show foils, flotation members, a drive system andsupport members in accordance with certain embodiments of the presentinvention;

FIGS. 34A-D show foils in accordance with certain embodiments of thepresent invention;

FIGS. 35A-D show flotation members, support members, foils, flexibledredging members and brushes in accordance with certain embodiments ofthe present invention;

FIG. 36 shows a foil, flotation member and support members that arerotatably connected in accordance with certain embodiments of thepresent invention;

FIGS. 37A and B show a portion of a mixing system having a camberedhorizontal support member in accordance with certain embodiments of thepresent invention;

FIG. 38 shows foils, flotation members, support members and a surfaceagitating comb in accordance with certain embodiments of the presentinvention;

FIG. 39 shows foils, flotation members and support members in accordancewith certain embodiments of the present invention;

FIG. 40 shows a portion of a mixing system and an airfoil in accordancewith certain embodiments of the present invention;

FIG. 41 shows a comparison of calculated energy requirements for mixingsystems of the present invention with a mixing system known in the art;

FIG. 42 shows a comparison of energy consumption in pneumatic andhydraulic mixing systems in accordance with certain embodiments of thepresent invention;

FIG. 43 shows an exemplary graphical representation of the dependence ofbiomass accumulation on mixing type in closed photobioreactors;

FIG. 44 shows an exemplary graphical representation of capitalexpenditure per hectare for different mixing systems;

FIG. 45 shows a perspective view of tethered drive elements inaccordance with certain embodiments of the present invention;

FIG. 46 shows a side view of an embodiment of the present inventionadapted to produce a breaking wave in shallow liquid;

FIG. 47 shows a side view of an embodiment of the present inventionproducing a breaking wave in shallow liquid; and

FIG. 48 shows a perspective view of an embodiment of the presentinvention producing a breaking wave in shallow liquid.

DETAILED DESCRIPTION OF EMBODIMENTS Mixer Drive System Design

FIGS. 1-4 show sectional, perspective and front views of a tubularfollower member 120. In the exemplary embodiment, the tubular followermember 120 is disposed around a portion of a drive conduit 100, suchthat the follower member 120 slides along the surface of the driveconduit 100 in a longitudinal direction. The follower member 120partially encloses a magnetic follower element 110, which is adapted toslide within the follower member 120 along the surface of the driveconduit 100 in a longitudinal direction. The distal end portions 192 ofthe follower member 120 are partially enclosed, thereby restricting themovement of the follower element 110 and providing surfaces againstwhich the follower element 110 can exert force.

The follower member 120 and drive conduit 100 can be constructed from,for example, blow-molded or injection-molded thermoplastic, or any othermaterial that is suitably rigid and light-weight.

FIGS. 5A and B show perspective and sectional views of an exemplaryfollower element 110, comprising magnets 140, a bushing 150 and anenclosure 160. The annular axial cross-section of the bushing 150enables the follower element 110 to slide axially along the driveconduit 100.

The bushing 150 can be constructed from, for example, stainless steel orany other material that is suitably resistant to wear and has a lowcoefficient of friction. The enclosure 160 can be constructed from, forexample, polyethylene or any other material that is suitably durable andhas a low coefficient of friction.

FIG. 6 illustrates a sectional view of a portion of an exemplary foilassembly 180 of the present invention. In certain embodiments, the drivesystem utilizes magnetic coupling between a drive magnet 142 or driveferromagnet 144 contained within the drive conduit 100 and a followermagnet 140 disposed outside the drive conduit 100, within the followermember 120, wherein the magnetic coupling is used in conjunction with amotive force, such as a pneumatic force or a hydraulic force, to propelthe foil assembly 180 through a mixing vessel.

In the exemplary embodiment, a tubular follower member 120 is disposedaround a portion of a drive conduit 100, such that the follower member120 slides along the surface of the drive conduit 100 in a longitudinaldirection. The follower member 120 is connected to a hydrodynamiccambered foil 170 by a support member 130. The distal end portions 192of the follower member 120 are partially enclosed.

In the exemplary embodiment, the follower magnet 140 is a ring magnetthat encompasses the circumference of the exterior surface of the driveconduit 100. The follower magnet 140 is adapted to slide within thefollower member 120 along the surface of the drive conduit 100 in alongitudinal direction. The partial enclosures of the end portions 192of the follower member 120 restrict the movement of the follower magnet140 relative to the follower member 120 and provide surfaces againstwhich the follower magnet 140 can exert force.

The drive magnet 142 or drive ferromagnet 144 is disposed within thedrive conduit 100 and is adapted to move longitudinally within the driveconduit 100 when motive force is applied to the drive magnet 142 ordrive ferromagnet 144.

In operation, a motive force is applied to the drive magnet 142 or driveferromagnet 144, which traverses the drive conduit 100 in a longitudinaldirection. The follower magnet 140 is magnetically coupled with thedrive magnet 142 or drive ferromagnet 144 and moves in unison with thedrive magnet 142 or drive ferromagnet 144. When the follower magnet 140comes into contact with the partial enclosure of either end portion 192of the follower member 120, the momentum of the follower magnet 140 istransferred to the follower member 120, which is propelled by thefollower magnet 140 and slides along the length of the drive conduit100. The foil 170 is connected to, and moves with, the follower member120, such that the foil 170 traverses through the mixing vessel and theliquid mixture contained therein in a linear path.

The direction in which motive force is applied to the drive magnet 142or drive ferromagnet 144 can be reversed, inducing the drive magnet 142or drive ferromagnet 144 to move in the opposite longitudinal direction.The follower magnet 140 is magnetically coupled with the drive magnet142 or drive ferromagnet 144 and correspondingly changes direction ofmotion with the drive magnet 142 or drive ferromagnet 144. Immediatelyafter the initial change of direction of motion, the follower magnet 140disengages from contact with the partial enclosure of the end portion192 of the follower member 120 and traverses the open interior portionof the follower member 120, during which the follower member 120 willremain stationary, or will not otherwise undergo motion attributable tothe follower magnet 140. If movement of the follower magnet 140 issustained, the follower magnet 140 subsequently comes into contact withthe opposite partially enclosed end portion 192 of the follower member120 and transfers momentum to the follower member 120. The followermember 120 and attached foil 170 consequently undergo a change ofdirection of motion.

In the exemplary embodiment, the distance between the position of thepartially enclosed end portion 192 of the follower member 120 and thevertical centerline of the support member 130 creates a locus of force,or tow point, between the follower magnet 140 and follower member 120that is forward of the foil 170 relative to the direction of motion ofthe foil assembly 180. When the direction of motion reverses, the towpoint becomes the point of contact between the follower magnet 140 andthe opposite end of the follower member 120, which is likewise forwardof the foil 170 relative to the direction of motion of the foil assembly180. This configuration enhances guidance and stability of the followermember 120 and the attached foil 170 by preventing yaw of the foilassembly 180 while the follower member 120 is motion in eitherdirection.

FIGS. 7A-H illustrate exemplary suitable drive magnets 142 or driveferromagnets 144 and follower magnets 140. Each drive magnet 142 ordrive ferromagnet 144 is disposed within a drive conduit 100 and isadapted to move within the drive conduit 100 in a longitudinal directionin response to a motive force applied to the drive magnet 142 or driveferromagnet 144. The drive magnets 142 or drive ferromagnets 144comprise, for example, one or more ferromagnetic ball bearings, one ormore axially-magnetized cylindrical magnets, or one or more sphericalmagnets. One of skill in the art will understand that the drive magnet142 or drive ferromagnet 144 can be made of any material and have anyshape suitable to promote magnetic coupling with the follower magnet 140and range of motion within the drive conduit 100. In some embodiments,the drive magnet 142 or drive ferromagnet 144 comprises steel, aneodymium iron boron magnet or another rare earth magnet. In someembodiments, the drive magnet 142 or drive ferromagnet 144 is coatedwith felt or other materials that are suitable for suppressing corrosionor wear of the drive magnet 142 or drive ferromagnet 144 and othersurfaces that come into contact with the drive magnet 142 or driveferromagnet 144.

In certain embodiments, the drive conduit 100 is a tube having acircular cross section and is made of low density polyethylene, highdensity polyethylene, cross-linked polyethylene, polyvinyl chloride,copper, steel or any other suitable material. In some embodiments, theconstruction of the drive conduit 100 provides positive buoyancy to helpmaintain the position of the drive conduit 100 relative to the surface320 of the liquid mixture.

The follower magnet 140 is disposed on or around the external surface ofthe drive conduit 100 in a manner that allows the follower magnet tomove along the longitudinal axis of the drive conduit 100. An example ofa suitable follower magnet 140 is one axially-magnetized ring magnet,wherein the ring magnet circumferentially encompasses a portion of thedrive conduit 100. Another suitable configuration is a plurality offollower magnets 140 embedded in a follower element 110 in the form of asliding sleeve. In some embodiments, the follower member 120 does notfully encircle the drive conduit 100. In some embodiments, the followermagnets 140 are disposed on opposite sides of the drive conduit 100 andare equidistant apart relative to the circumference of the drive conduit100. One of skill in the art will understand that the follower magnet140 may be made of any material and have any shape suitable to promotemagnetic coupling with the drive magnet 142 or drive ferromagnet 144 andlongitudinal range of motion along the exterior of the drive conduit100. In some embodiments, the follower magnet 140 comprises a neodymiumiron boron magnet or another rare earth magnet.

In the present invention, the gap between the surface of the drivemagnet 142 or drive ferromagnet 144 and the interior surface of thedrive conduit 100 is minimized in order to reduce hydraulic or pneumaticfluid flow around the drive magnet 142 or drive ferromagnet 144 andmaximize motive force applied to the drive magnet 142 or driveferromagnet 144 and the foil 170 for a selected flow rate of drivefluid. In certain embodiments comprising a pneumatic fluid used to applymotive force to the drive magnet 142 or drive ferromagnet 144, a lowfriction seal between the surface of the drive magnet 142 or driveferromagnet 144 and the interior surface of the drive conduit 100 isutilized. The low friction seal can be created by, for example,dispersing oil along the length of the interior surface of the driveconduit 100 or by applying a ferromagnetic fluid to the surface of thedrive magnet 142 or drive ferromagnet 144. In certain embodiments, feltor another suitable material or coating is adhered or applied to thesurface of the drive magnet 142 or drive ferromagnet 144 to reducefriction between the drive magnet 142 or drive ferromagnet 144 and theinner surface of the drive conduit 100.

FIG. 8 shows a sectional view of a drive element 190 disposed within adrive conduit 100. The drive element comprises a drive magnet 142 ordrive ferromagnet 144 embedded in a plug of closed cell foam 200,wherein the shape of the plug of closed cell foam 200 conforms to theinner surface of the drive conduit 100. The drive element 190 furthercomprises inserts of open cell foam 210 embedded within the plug ofclosed cell foam 200. The inserts of open cell foam 210 are positionedand adapted to expand and exert outward pressure on the plug of closedcell foam 200 in order to improve sealing and decrease empty spacebetween the outer surface of the drive element 190 and the inner surfaceof the drive conduit 100.

FIGS. 9 and 10A-C show another embodiment of a drive element 190,comprising a drive magnet 142 or drive ferromagnet 144, an O-ring 220,an insert 230, a ring 240 and an end cap 250. The o-ring 220 may be madeof, for example, nitrile rubber. The insert 230 may be made of, forexample, nylon 6-6. The ring 240 may be made of, for example,polytetrafluoroethylene. The end cap 250 may be made of, for example,nylon 6-6. The outside diameter of the O-ring 220 is slightly largerthan the inside diameter of the drive conduit 100. The o-ring gland 232in the insert 230 in which the O-ring 220 sits is wider than thediameter of the O-ring 220, and the inside diameter of the o-ring 220 isslightly larger than the diameter of the o-ring gland 232 in which theO-ring 220 sits, such that the O-ring 220 sits loosely in the O-ringgland 232. When the drive element 190 is disposed in the drive conduit100, the o-ring 220 is squeezed against the inside wall of the driveconduit 100 but is free to move laterally in the o-ring gland 232 (FIG.10B). Pneumatic motive force applied to the drive element 190 forces theo-ring 220 to move in the direction of the motive force until itcontacts the wall of the o-ring gland 232, forming a floating sealbetween the o-ring 220, the wall of the o-ring gland 232 and the innerwall of the drive conduit 100 (FIG. 10C).

FIGS. 11A-C and 12A-D show a drive element 190 that incorporates abypass adapted for use with a mixing system that incorporates ahydraulic form of motive force. The drive element 190 has an annularshape, and a plunger 260 is disposed at least partially within the driveelement 190 such that the plunger 260 can slide laterally within thedrive element 190. When the plunger 260 is positioned such that neitherhead 262 is in contact with the drive element 190, fluid can flow aroundthe plunger 260 and through the annular opening in the drive element 190(FIG. 11C).

A cap 270 may be sized and positioned within the drive conduit 100 suchthat the cap 270 restricts the lateral motion of the drive element 190.The cap 270 may be configured so as to hold the plunger 260 in the openposition when the cap contacts the drive element 190, such that fluidflows through the annular opening in the drive element 190 and throughcorresponding channels 272 formed in the cap 270. If any blockage occursin the drive system, the configuration shown in FIGS. 11A-C and 12A-Dprevents excess fluid pressure from accumulating.

As illustrated in FIG. 13, the towing point for rigidly mounted foils170 is shifted forward of the flotation members 300, which act asrudders to provide steering, when the direction of movement of the foilassembly 180 is reversed. The exemplary embodiment illustrated in FIG.13 allows the tow point of the foil assembly 180 to slide to a stopbeyond the flotation members 300 by allowing the follower element 110 toslide along the drive conduit 100 between end caps 122 that are mountedin fixed positions on the drive conduit 100. Pads 280 may be attached tothe follower element 110 or end caps 122 to reduce the force of impactcaused by acceleration of the foil assembly 180 during a reversal in thedirection of motion. The impact force may also be reduced byincorporating an alternative attachment between the foil 170, flotationmember 300 or support members 130 and the end caps 122. The attachmentmay incorporate flexible tension members 290 made of, for example, 0.125inch-diameter silicon rubber, under slight tension. The tow point inthis exemplary embodiment also alternates as a steering element orstabilizing rudder when it is shifted aft of the foil 170.

FIGS. 14, 15, 16 and 17A-G illustrate alternative embodiments of mixingvessels containing liquid algae cultures and mixing systems inaccordance with the present invention. In FIGS. 14 and 15, the driveconduit 100 is disposed in or above the surface 320 of the algae cultureso that it floats in the photobioreactor 310. The drive conduit 100 maybe made from, for example, high density polyethylene or any othersuitable material that is inexpensive and is durable in saltwater,volatile compounds, sterilizing agents and moderate heat. In theexemplary embodiments, the follower element 120 contains followermagnets 140. Magnets of 0.5 inch diameter and 0.5 inch length canachieve a coupling force of four pounds with minimal lateral forceacting on the drive magnet 142 or drive ferromagnet 144, which would beexhibited as friction between the drive magnet 142 or drive ferromagnet144 and the inner wall surface of the drive conduit 100. The exemplaryembodiments also incorporate horizontal support members 130 positionedabove the surface 320 of the algae culture to reduce hydrodynamic drag,and vertical support members 130 connecting the flotation members 300 tothe foils 170 that are adapted to minimize interference with fluid flowaround the foils 170.

In some embodiments, the drive conduit 100 is located outside the mixingvessel, and the drive element 190 contained therein is magneticallycoupled to a foil assembly 180 disposed inside the mixing vessel. Asshown in FIG. 16, the drive conduit 100 is disposed underneath thebottom surface of the photobioreactor 310. The film of thephotobioreactor 310 lays over the drive conduit 100 and a track 352. Theweight of the algae culture provides sufficient hydraulic pressure tofix the position of the drive conduit 100 and the track 352. A wheeledcarrier 350 inside the photobioreactor 310 longitudinally traverses thetrack 352 and carries a follower magnet 140 that is magnetically coupledwith a drive magnet 142 or drive ferromagnet 144 disposed within thedrive conduit 100. An array of foils 170 are attached to the wheeledcarrier 350. In some embodiments, the drive conduit 100 and the track352 are welded or otherwise fixed to the film of the bioreactor 310.

Sufficient vertical and horizontal clearances between the wheeledcarrier 350 and the track 352 are maintained to accommodate for theconformation of the film around the track 352. In the exemplaryembodiment, a set of 3, 0.5 inch long follower magnets 140 provides 2pounds of coupling force in the axial direction, which is sufficient tomaintain coupling during sudden decelerations of the drive element 190when stopped or started at the ends of the photobioreactor 310. Thisarrangement of follower magnets 140 also provides a torque and downwardattraction force of approximately 4 pounds that prevents the wheeledcarrier 350 from separating from the track 352.

The embodiments illustrated in FIGS. 14 and 15 eliminate the need to laythe film of the photobioreactor 310 carefully over the drive conduit 100in the embodiment of FIG. 16 in order to avoid wrinkles that mightstructurally compromise the film of the photobioreactor 310 and the needto have a flat track 352 underneath the photobioreactor 310. In theembodiments of FIGS. 14 and 15, there is no wheeled carrier 350 rollingon the floor of the photobioreactor 310, so the thin film of thephotobioreactor 310 is not exposed to continual mechanical stress on itssurface, which eventually may lead to failure of the film.

Photobioreactors 310 also may deflect horizontally over lengths of, forexample, 50 feet. With the exemplary embodiment illustrated in FIG. 16,deflection of more than a few inches may cause a foil 170 to impact thefilm on the side of a photobioreactor 310 and potentially tear the film,if no guard mechanism is in place, and if the drive conduit 100 and thetrack 350 are not fixed to an inside surface of the bioreactor 310. Inthe embodiment illustrated in FIG. 15, if the photobioreactor 310 curvesexcessively, the wall of the photobioreactor 310 would push the trackingmember 340 above the surface 320 of the algae culture and displace thefoil assembly 180 laterally, since the drive conduit 100 would offerminimal bending resistance. The tracking members 340 thereby guardagainst accidental contact between the foils 170 and the film on thesides of the photobioreactor 310.

FIGS. 17A-C illustrate exemplary embodiments having a drive conduit 100positioned underneath, or on any side of, a photobioreactor 310. One ormore drive magnets 142 or drive ferromagnets 144 are contained in thedrive conduit 100. One or more follower magnets 140 are attached to aflotation member 300 by support members 130 and are magnetically coupledwith the drive magnets 142 or drive ferromagnets 144.

Motive Force System

The present invention utilizes a pump 420 to provide motive force to thedrive elements 190 in an array of mixing vessels, such asphotobioreactors 310. In some embodiments, one pump 420 can drive mixingin multiple vessels.

The pump 420 moves drive fluid through the drive conduit 100. The drivefluid may be, for example, air, water, mineral oil or polyethyleneglycol, and the drive fluid may be suffused with agents that inhibitcorrosion. In some embodiments, a drive fluid of low density is selectedfor use in the drive conduit 100 to promote positive buoyancy of thedrive conduit 100, in particular if the drive conduit 100 is constructedof materials having high density, such as steel or iron.

FIGS. 22 and 24 show exemplary embodiments in which a drive conduit 100served by a single pump 420 and a switching valve 430 is routed throughmultiple photobioreactors 310 in a serpentine configuration. One or moredrive elements 190, follower elements 110 and foil assemblies 180 can bedisposed inside each photobioreactor 310. In the exemplary embodiment,the pump 420 and switching valve 430 are located outside thephotobioreactors 310 and the drive system is closed.

FIG. 22 illustrates an exemplary hydraulic mixing system in which onepump 420 drives mixing in four rows of at least 70 photobioreactors 310per row. Each row of photobioreactors 310 is partitioned into groups of12 photobioreactors 310 through which a single drive conduit 100 of 0.5inch diameter passes. Row is distributed to the rows of photobioreactors310 via the drive conduits 100 using a two inch diameter pipe 410. Apump 420 pushes water through the pipes 410 and drive conduits 100 todrive one or more drive elements 190 in the drive conduits 100 in eachphotobioreactor 310. The drive elements 190 are magnetically coupled tofoil assemblies 180, which comprise follower elements 110, followermembers 120, foils 170 and connecting support members 130.

The exemplary hydraulic mixing system of FIG. 22 comprises a pump 420rated at one horsepower, 48 gallons per minute and 200 foot head(approximately 100 pounds per square inch). The exemplary hydraulicmixing system further comprises a four-way air piloted valve 430 adaptedto switch the direction of hydraulic flow, a flow control valve 440, aflow meter 450 and an air bleed tank 460. The hydraulic pressure in thepipe 410 is approximately 30 pounds per square inch.

The exemplary hydraulic mixing system of FIG. 22 moves the driveelements 190 and foil assemblies 180 at a constant speed for apreselected length of time. In some embodiments, a length of timegreater than 30 seconds is expected to be sufficient for the driveelements 190 and foil assemblies 180 to traverse the full length of aphotobioreactor 310. Mechanical stops (not shown) at the ends of eachphotobioreactor 310 restrict the movement of the drive elements 190 andfoil assemblies 180 while hydraulic flow continues for a short period oftime to enable the drive elements 190 and foil assemblies 180 to reachthe end of each photobioreactor 310. In some embodiments, the shortperiod of time is five to ten seconds.

In the exemplary hydraulic mixing system, the four-way air piloted valve430 subsequently is activated to reverse the hydraulic flow throughoutthe drive conduit 100. The activation of this valve 430 preferablyoccurs slowly enough to avoid dislodging the magnetic coupling betweenthe drive elements 190 and follower elements 110. In some embodiments,the length of time for activation of the valve 430 is greater than 100milliseconds.

In alternative embodiments, a reversible positive displacement pump 420with a variable frequency drive is used and the four-way air pilotedvalve 430 is omitted. The hydraulic flow through the system iscontrolled to a specified rate.

Energy usage can be reduced by reducing the cross-sectional area of thedrive conduit 100 or changing the drive fluid to air. Reducing thecross-sectional area of the drive conduit 100 requires closer tolerancesbetween the drive element 190 and follower element 110 so that smallermagnets can be used. Changing the drive fluid to air requires using asealing fluid around the drive magnet 142 or drive ferromagnet 144 toavoid wasting energy.

FIG. 23 illustrates an exemplary pneumatic mixing system in which onepump 420 drives mixing in 240 photobioreactors 310 connected inparallel. Drive conduits 100 of 0.5 inch diameter pass through each rowof photobioreactors 310. Flow is distributed to the rows ofphotobioreactors 310 via the drive conduits 100 using a two inchdiameter pipe 410. A pump 420 pushes air through the pipe 410 and driveconduits 100 to drive one or more drive elements 190 in the driveconduits 100 in each photobioreactor 310. The drive elements 190 aremagnetically coupled to foil assemblies 180, which comprise followerelements 110, follower members 120, foils 170 and connecting supportmembers 130.

In some embodiments, a system of the present invention incorporatesmultiple drive elements 190 and foil assemblies 180 in one mixingvessel. The foil assemblies 180 are disposed on the drive conduit 100 atselected distance intervals and are driven by the same motive system.The foil assemblies 180 may be configured and spaced to provide mixingover the full length of the mixing vessel, wherein each foil assembly180 provides mixing for a selected portion of the mixing vessel. One ofordinary skill will appreciate that the lowest energy consumptionrequired to achieve a desired degree of vertical mixing in aphotobioreactor 310 can be determined by varying the number andconfiguration of foil assemblies 180 that are used in thephotobioreactor 310.

FIG. 24 illustrates an embodiment in which multiple photobioreactors 310are serviced by one pump 420 and one drive conduit 100. Thephotobioreactors 310 are connected in series. In this embodiment,multiple foil assemblies 180 are disposed inside each photobioreactor310 and are configured to traverse the length of the bioreactor inopposite directions.

AG. 25 illustrates an embodiment in which multiple photobioreactors 310are serviced by one pump 420 and multiple drive conduits 100 that arefed by a header pipe 410. Pairs of photobioreactors 310 are connected inparallel, and the photobioreactors 310 in each pair are connected inseries. In this embodiment, multiple foil assemblies 180 are disposedinside each photobioreactor 310 and are configured to traverse thelength of the bioreactor in the same direction.

In embodiments of the present invention that utilize pneumatic force tomove foil assemblies 180, multiple foil assemblies 180 may be disposedinside each photobioreactor 310, while multiple photobioreactors will beconnected in parallel, instead of in series. As shown in FIG. 45,multiple drive elements 190 are tethered by a connector 252, which maybe any flexible or rigid elongate member made of, for example, plastic,nylon or elastomer, that physically connects the drive elements 190.Unidirectional floating seal grooves 222 are formed in the driveelements 190 positioned at the distal end of each chain of driveelements 190. When pneumatic motive force is applied, the unidirectionalfloating seal groove 222 formed in the drive element 190 in the upstreamposition allows gas to slip underneath the o-ring 220 and prevent theformation of a seal. A seal is instead formed by the o-ring 220 presentin the downstream drive element 190. The downstream drive element 190moves in the direction of the pneumatic motive force and pulls theupstream drive element 190 in the same direction. If the chain of driveelements 190 includes three or more drive elements 190, then only thedrive element 190 at the upstream end of the chain and the drive element190 at the downstream end of the chain have a-rings 220, so that noseals are formed by the drive elements 190 positioned in the interior ofthe chain.

In embodiments of the present invention that utilize hydraulic force tomove foil assemblies 180, a disadvantage of servicing multiple vesselsin series using one pump 420 is that an increased pressure drop causedby a decreased rate of mixing in one vessel, such as due to a stoppeddrive element 190, affects mixing speed in all other vessels in thearray. In some embodiments, a system of the present invention comprisesa positive displacement pump 420, such as a vane pump, for the purposeof rendering flow rate through the pump 420 independent of pressurevariations and providing consistent mixing speed in the array ofvessels.

Operating pressure in a system of the present invention utilizinghydraulic force is approximately 32 pounds per square inch, whilemaximum pressure induced by stoppages of the drive elements 190 intwelve mixing vessels may be as high as 360 pounds per square inch. Alarge pump motor 420 may generate sufficient torque to maintain constantmixing speed under temporary large pressure drops in the mixing systembut will not operate efficiently under smaller pressure drops that aretypical during normal operation of the mixing system, when no driveelements 190 are stopped. With reference to FIG. 18, in someembodiments, the conduit used in a system of the present inventionallows flow past a stopped drive element 190 and reduces the pressuredrop, which reduces the size of the pump motor 420 needed for thesystem, by incorporating a small channel 360 between the surface of thedrive element 190 and the inner surface of the drive conduit 100. Thechannel 360 is sufficiently small to maintain motive force in the formof pressure from a drive fluid applied to the drive element 190 undernormal operation, and the change in outside diameter of the driveconduit 100 is sufficiently small to avoid interference with a followerelement 110. If channels 360 are formed in the inner surface of thedrive conduit 100 and the outside diameter of the drive conduit 100 isunchanged, a higher schedule drive conduit 100 must be selected tocompensate for the loss of pressure capability in the drive conduit 100.

As illustrated in FIGS. 19A and B and FIGS. 20A and B, in someembodiments, the drive element 190 incorporates a poppet valve 370. If amisaligned or otherwise impeded drive element 190 creates a blockage inthe drive conduit 100, the poppet valve 370 is adapted to allow drivefluid to flow through the drive element 190 and provides an alternativemeans of releasing pressure. In some embodiments, the internal surfaceof the drive conduit 100 incorporates drive stops 380 that restrict themotion of the drive element 190 in a longitudinal direction within thedrive conduit 100. In some embodiments, a valve opening pin 390 isadapted to actuate the poppet valve 370.

As illustrated in FIGS. 21A and B, some embodiments comprise a bypassconduit 400 that is formed in the drive conduit 100. The bypass conduit400 is adapted to relieve fluid pressure by diverting the flow of drivefluid in the event that a blockage occurs in the drive conduit 100between the inlet and outlet of the bypass conduit 400. In someembodiments, the follower member 120 is shaped to accommodate theplacement of the bypass conduit 112.

As illustrated in FIGS. 26, 27 and 28, in some embodiments the motivesystem is a cable connected system. A cable 470 attaches to a foil 170and/or to flotation members 300 in a foil assembly 180. The cable 470 ispulled by a motor 472 that is configured to pull the cable 470 in morethan one direction. The foil 170 is moved by actuating the motor 472 topull the cable 470, and the cable 470 is wound on a spool 474 at eitherend of the mixing vessel depending on the direction of travel.

Foil Design

A system in accordance with certain embodiments of the present inventioncomprises a surface, or foil 170, that is shaped to provide hydrodynamiclift, wherein the foil 170 can be moved through an aqueous culture ofalgae to efficiently generate a vertical movement of algae. FIGS. 14,15, 16 and 28 illustrate exemplary foils 170 used in a mixing system ofthe present invention. It is desirable to induce flow with the lowestvelocity needed to provide satisfactory mixing while minimizing energyconsumption. Net vertical flow of the aqueous culture in the mixingvessel is zero. In the lowest energy case, upward and downwardvelocities are equal and act over equal areas.

FIG. 14 illustrates idealized vertical fluid motion in trailing vortices330 generated by foils 170 in a photobioreactor 310. The trailingvortices 330 remain stationary in the middle of the photobioreactor 310due to net cancellation of induced velocity from image vortices (notshown) that are created at the top and bottom of the aqueous culture.Generating trailing vortices 330 in the center of the photobioreactor310 may maximize the mixing length, or vertical particle displacement,over which the vortices 330 can transport flow. Trailing vortices 330 inthe center of the photobioreactor 310 form a stable arrangement and tendnot to migrate in location. In contrast, pairs of counterrotatingvortices 330 move vertically in unbounded flows or move laterally near ahorizontal surface.

In the exemplary embodiment, foils 170 distributed along the span of aphotobioreactor 310 provide a regular arrangement of mixing vortices 330that minimize the presence of dead zones with no mixing. Such mixing issufficient to sustain algae cultures over extended periods of time.Aqueous algae cultures can die from anoxia due to reduced gas exchangeand sedimentation of the algae if mixing is stopped for a period ofseveral hours.

A foil assembly 180 generally may be moved at a higher speed withdownwardly concave foils 170, instead of upwardly concave foils 170.However, downwardly concave foils 170 produce trailing vortices 330 thatinduce sedimentation of algae in regions away from the foils 170, whileupwardly concave foils 170 produce trailing vortices 330 that rotate inthe opposite direction and induce sedimentation of algae in the regionunderneath the foil 170. Additional mixing and resuspension of settledalgae may be facilitated to a greater extent by a pattern ofsedimentation underneath the foil 170 rather than sedimentation awayfrom the edges of the foil 170.

The migratory speed of trailing vortices 330 can be predicted bydetermining the velocity a vortex 330 will induce on its neighbor,according to potential flow theory and in situations with surfaces,including the effect of image vortices. For a vortex 330 near a singlehorizontal surface, such as the bottom of the photobioreactor 310, theimage vortex (not shown), which is a vortex 330 with opposite rotationplaced equidistant but on the opposite side of the horizontal surface,will induce the actual vortex 330 to move laterally with a certainspeed. When the actual vortex 330 is bounded on the opposite side by asecond horizontal surface, which is the top surface 320 of the liquidmixture in exemplary embodiments of the present invention, the imagevortex from this surface 320 will induce a directed motion counteringthe induced motion from the lower surface. If the vortex 330 is centeredbetween these two surfaces, then the induced effect cancels completelyand the vortex 330 remains stationary. The stability of the vortex 330position allows for subsequent passes of a foil 170 to reinforce thestrength of the vortex 330.

The trailing vortices 330 decay slowly and are continually reinforced asthe foils 170 longitudinally traverse the photobioreactor 310 in eitherdirection, allowing the foils 170 to effectively mix a large area ofaqueous culture in the vessel compared to the planform area of each foil170. This efficiency reduces the amount of equipment needed for mixingand capital costs.

The preferred placement of the foil 170 is middepth in the aqueousculture, with the span of the foil 170, and the lateral spacing betweenfoils 170, equal to the depth of the culture. This placement produces astable configuration of trailing vortices 330.

The trailing vortices 330 are strengthened by increasing the liftgenerated by the foil 170. Lift is controlled by the planform area,angle of attack, camber and speed of the foil 170. The trailing vortices330 are also reinforced by multiple passages of each foil 170, which canbe increased by increasing foil 170 speed for a photobioreactor 310 of afixed length or by employing multiple foil assemblies 180 along thelength of one photobioreactor 310. Foils 170 can be spaced equidistantalong the transverse axis of the photobioreactor 310 to reduce the timeover which a trailing vortex 310 will decay before reinforcement andthereby achieve desired recirculation with uniformity and low powerrequirements.

FIG. 29 illustrates measurements of a trailing vortex 330 pair generatedby a single foil 170 in an algae culture having a depth of eight inches.The particle traces shown cover the depth of a photobioreactor 310,eight inches, and show the flow pattern of the particles after thepassage of one foil 170. Movement of the foil 170 (not shown) is in aplane perpendicular to the plane of the image. The trailing vortices 330were generated by the distal ends of a foil 170 designed to producesimilar recirculation times in the aqueous culture when the foil 170longitudinally traverses the photobioreactor 310 at mid-depth in thealgae culture. The foil 170 shape is symmetric and cambered to generatea vortex 330 system with rotations that are independent of the directionof traverse. The trailing vortices 330 were measured through laserdiagnostics. The particles are neutrally buoyant and were illuminatedwith a laser light sheet. Four consecutive exposures are superimposed inthis image to show the movement of the particles over intervals of 66.7milliseconds. Total plotted time for each particle is therefore 4×66.7milliseconds=0.26 seconds.

FIG. 30 illustrates a computational simulation of trailing vortices 330generated by a foil 170 passing through an algae culture with a depth ofeight inches. This image provides the same view of particle traces shownin FIG. 29. Each trace in FIG. 30 represents a total travel time of 8.21seconds per particle. Particles in this simulation are nonuniformlydistributed at an initial time measurement, with most of the particlesbeing located at mid-depth in the algae culture in a photobioreactor 310at time=0 seconds. For a given position along the length of the algaeculture in the photobioreactor 310, the vortices 300 decay over time andmust be reinforced or regenerated by the periodic passage of the foil170. The maximum time to reinforce trailing vortices 330 is roughly 30seconds between passages for a foil 170 travelling at 0.5 meters persecond.

In some embodiments, the foil assembly 180 comprises a symmetric,cambered foil 170. One of skill in the art will recognize that otherconfigurations are also suitable to produce effective mixing andgenerate trailing vortices 330. Trailing vortices 330 can be generatedby hydrodynamic drag on flat foils 170 that have no camber and are heldat a constant angle of attack as the foils 170 traverse aphotobioreactor 310, FIG. 31 illustrates a foil 170 with a quadrangularplanform shape that can produce hydrodynamic lift.

FIGS. 32A and B illustrate exemplary foils 170 that are mounted on axles510 connected to the foil assembly 180 and are adapted to swivel orpivot to an inclined orientation. The angle of attack, or pitch, of thefoil 170 may be maintained by differential weighting along the chord ofthe foil 170. Triangular and quadrangular planform shapes are suitablefor foils 170 of these embodiments. Differential weighting between thesum of the hydrodynamic lift and the weight of the foil 170 may beadjusted by incorporating a weight 480, or an interstitial space 490,embedded in the foil 170. The angle of attack and the amount ofcirculation generated may thereby be varied and adjusted.

With respect to foils 170 that incorporate embedded weights 480, caremust be taken to ensure that the trailing edges of foils 170 with longchords do not scrape the bottom of the mixing vessel during a reversalin travel direction of the foil 170, as the foil 170 swings underneaththe axle 510. With a buoyant trailing edge incorporating an interstitialspace 490, this is avoided since the trailing edge of the foil 170 wouldswing over the axle 510.

With reference to FIGS. 32A and B, foils 170 that swivel preferablyincorporate a rudder 500 to prevent yaw while avoiding the need to pullthe foil 170 from a shifting forward location.

FIGS. 33A and B illustrate an embodiment comprising foils 170 positionedin a vertical orientation. Trailing vortices 330 can be generated byvertical foils 170 that are oriented at slight angles to the directionof the foil 170 movement. In some embodiments, the vertical foils 170have a triangular planform shape.

In some embodiments, foils 170 are made from molded plastic, fiberglass,sintered nylon, glass-reinforced plastic, or any other material that issuitable to provide rigidity, durability, and positive or neutralbuoyancy.

FIGS. 34A-D illustrate an embodiment comprising vertically-orientedfoils 170 that are designed increase the extent of mixing directlybeneath a horizontally-oriented, upwardly concave foil 170 in regionwhere settling may occur. The two vertically-oriented foils 170 are setin opposition to yield net zero horizontal lift. The twovertically-oriented foils 170 create a set of trailing vortices 330 thatimpinge on the liquid culture directly beneath the vertically-orientedfoils 170 and create a high shear zone that promotes mixing and reducessedimentation beneath the foils 170.

FIGS. 35A and B illustrate the use of a chain 520 or other suitableflexible dredging member to reduce sedimentation in the aqueous culture.In this exemplary embodiment, a chain 520 is attached to, and suspendedfrom, the foil 170 and drags through the space beneath the foil 170where sediment accumulates.

If sedimentation is a more severe problem than the need for verticalmixing, foils 170 can be omitted from the foil assembly 180 and auniform brush 530 can be attached to the foil assembly 180 instead, asillustrated in FIGS. 35C and D. The density of the brush 530 bristlesmust be sparse enough to avoid excessive hydrodynamic drag forces.Sufficient downward force must be applied to the brush 530 by, forexample, utilizing the weight of the support to scrape settled algaefrom the bottom of the mixing vessel.

As illustrated in FIG. 36, a foil 170 can be rotatably attached to avertical support member 130 at a pivot point 540. When the foil 170 istraversing the photobioreactor 310, the opposing force exerted by thealgae culture causes the foil 170 to rotate away from the direction oftravel, thereby tilting the foil 170 and holding the foil 170 at anangle of attack. This effect creates hydrodynamic drag and turbulence atthe trailing edge of the foil 170, which enhances mixing. When the foil170 reverses direction, the foil 170 swings in the opposite direction ina pendulum fashion and correspondingly creates turbulence and mixing inthe same manner.

Supporting Structure

There are several ways to maintain the foil 170 at a constant pitch andwith minimal roll. In an exemplary embodiment illustrated in FIG. 28,the foil 170 is attached to tensioned guidelines 470. Thin rods areattached to the leading and trailing edges of the foil 170.

In embodiments shown in FIG. 31 and FIGS. 35-0, the foil 170 is attachedto a flotation member 300, such as, for example, a pontoon, whichreduces frictional losses. The wave pattern generated by the leading endof the flotation member 300 additionally increases mixing at the surface320 of the algae culture to enhance gas exchange, light penetration andphotosynthesis. Counter-rotating longitudinal vortices 330 near thesurface 320 are also generated in the wake of the flotation member 300and can be enhanced by specific hull designs. The width and lateralweight distribution of the flotation member 300 control roll, which isessential to maintain the foil 170 at a constant depth, while the lengthof flotation member 300 controls pitching and thus the angle of attackof the foil 170.

As illustrated in FIGS. 37A and B, agitation of the surface 320 can beenhanced by inducing a small hydraulic lump 550 by towing a foil 170 ora cambered horizontal support member 130 just below the surface 320 ofthe algae culture.

As illustrated in FIG. 38, in some embodiments, a surface agitating comb560 or other suitable ancillary structure is attached to a horizontalsupport member 130 to agitate the surface 320 of the algae culture andincrease gas transfer rates between vapor and liquid phases contained ina photobioreactor 310.

As illustrated in FIG. 39, in some embodiments, one or more verticalsupport members 130 connecting a foil 170 to a flotation member 300serve as rudders to prevent yaw. To be effective as steering devices,the foil 170 needs to pulled from a point forward of the center ofpressure for the vertical support members 130 acting as rudders. Alarger distance between the tow point and the center of pressure for thevertical support members 130 requires a stronger restoring force toalign the foil 170 and counter any imbalance caused by imperfect foil170 manufacturing, fouling from algae growth on the foil 170 or frictionfrom contacting a surface of the photobioreactor 310. The verticalsupport members 130 additionally agitate the surface 320 of the algaeculture.

In some embodiments, flotation members 300 and support members 130 aremade from molded plastic, fiberglass, sintered nylon, glass-reinforcedplastic, or any other material that is suitable to provide rigidity,durability, and positive or neutral buoyancy.

As illustrated in FIG. 40, in some embodiments, an airfoil 580 ispositioned above the surface 320 of liquid in a photobioreactor 310.This configuration advantageously induces circulation of the vapor phasein the photobioreactor 310, which helps to increase the efficiency of asolar still by enhancing vapor transport from the surface 320 of thewater to the walls of the photobioreactor 310.

In some embodiments, the longitudinal axis of the photobioreactor 310 orother mixing vessel is vertical. The drive conduit 100 likewise isvertically oriented, and the foil assembly 180 moves in a verticaldirection along the drive conduit 100 and is fully submersed in thecontents of the mixing vessel over at least a portion of the mixingvessel.

In some embodiments, the foil assembly 180 is used to skim the surface320 of an open pond. The drive conduit 100 is positioned at or near thesurface 320 of the pond, and the position and angle of attack of thefoil 170 is adapted to maintain the foil 170 at or immediately beneaththe pond surface 320.

In an exemplary embodiment, a gas sparging hose 700 is attached to afoil 170. Gas 702 may be pumped through the hose 700 and bubbled intothe algae culture, with the outlet of the hose 700 located, for example,underneath the foil 170, near an edge of the foil 170 or immediatelyunderneath the surface 320 of the algae culture. The hose 700 is adaptedto move along the length of the photobioreactor 310 with the foil 170.Movement of the foil 170 creates shear in the algae culture near thelateral edges of the foil 170, which shears and reduces the size of thegas bubbles 702. Additionally, the gas bubbles 702 are entrained in thetrailing vortices 330, which increases the residence time of the gasbubbles 702 in the algae culture and improves efficiency of masstransfer between the liquid phase of the algae culture and the gas phasepresent in the photobioreactor 310.

The hose 700 supplying the gas may be made of any suitable materialsthat are impermeable to the gas, that provide buoyance for the hose 700to float on the surface 320 of the algae culture and that aresufficiently pliable to enable the hose 700 to fold or coil on thesurface 320 of the algae culture. In some embodiments, a cageadditionally is attached to the foil assembly 180 to capture slack inthe hose 700 and prevent tangling.

In an exemplary embodiment, one or more Venturi tubes are incorporatedin support members 130, with one opening of each Venturi tube disposedabove the surface 320 of the algae culture and the opposite opening ofeach Venturi tube disposed below the surface 320 of the algae culture.The diameter of each Venturi tube may be, for example, approximately 1to 2 millimeters.

As the foil 170 moves through the algae culture, a pressure gradientdevelops across the length of the Venturi tube. The pressure gradientpulls gas into the algae culture from above the surface 320 of the algaeculture, creating small bubbles that are expelled into the algaeculture. In some embodiments, Venturi tubes in the support members 130are formed symmetrically to provide equivalent gas bubbling in eachdirection of longitudinal motion of the foil 170.

In an exemplary embodiment using pneumatic motive force to drive thedrive element 190, the foils 170, support members 130 and other parts ofthe foil assembly 180 are omitted and only a follower element 110, whichis magnetically coupled to the drive element 190, moves along the lengthof the drive conduit 100. When driven at high speeds, a cylindricalfollower element 110 creates an air cavity in the shape of a bell behindthe follower element 110 as it moves through the algae culture. Theplunging jet of the liquid bell causes the formation of small bubbles inthe algae culture, which increases mixing and mass transfer from thealgae culture.

In some embodiments in which the foil assembly 180 is omitted, a gassparging hose 700 is attached to the follower element 110. The hose 700introduces gas bubbles 702 into the algae culture. The end of the hose700 that is not attached to the follower element 110 may be connected tothe photobioreactor 310 along the side in the center of thephotobioreactor 310.

Mixing Operations

A mixing system in accordance with some embodiments of the presentinvention is capable of generating vertical mixing that is essential tothe cultivation of algae in a photobioreactor 310 while minimizingcapital investment and energy usage. In shallow depths with verticalrecirculation, the necessary minimum vertical velocity needed tomaintain a culture comprising certain strains of algae and to preventvisible sedimentation is approximately 20 to 30 seconds for turnover ofalgae in a circular cross section of six to eight inches contained in aculture having a depth of eight inches. For circulation rates thatexceed this threshold, production in these systems increases onlyslightly, while energy consumption increases significantly.

FIG. 41 illustrates calculated energy requirements for mixing in araceway pond system known in the art, as compared with energyrequirements for certain embodiments of the present invention, toaccount for sliding friction, hydraulic and pneumatic losses and motorefficiency. The system of the present invention advantageously consumesenergy at a lower rate while providing sufficient mixing of an aqueousalgae culture. The smaller and larger columns for the raceway systemrepresent, respectively, energy consumption required for 40 second and20 second turnover times. This range of circulation times corresponds tothe initial circulation time (20 seconds) after a foil assembly 180passes through a static point in the mixing vessel and the decayedcirculation time (40 seconds) immediately before the foil assembly 180subsequently passes through the same point again, when the foil assembly180 is towed at 0.5 meters per second.

A major distinction between rotary impeller motion known in the art andthe linear foil 170 motion comprised by the present invention is thefunctionality and performance of the type of motion. Rotary impeller, orpaddle wheel, motion is generally utilized to generate a directed flow,typically along the length or circumference of the vessel. Fluctuationsin motion that are transverse to the selected direction of flow arechaotic and occur due to turbulence that is generated in the boundarylayer of the vessel. Components of turbulence that are not directedvertically and do not contribute to vertical transport, which isimportant in the embodiment of a photobioreactor 310 where light isreceived from overhead, are nonetheless generated. The chaotic verticalmotion and extra fluctuation components thus make this rotary motionenergetically inefficient for bulk vertical transport.

The efficiency of vertical transport may be increased by placing foils170 in a stream (as taught by Laws et al.) to induce verticalrecirculation. However, the majority of flow kinetic energy is stilldissipated through overcoming boundary friction in sustaining therelative motion required.

In accordance with embodiments of the present invention, by moving thefoil 170 in a linear path through an algae culture contained in aphotobioreactor 310 or other mixing vessel, the problem of dissipationof flow kinetic energy is overcome. The decay of recirculation, which iscreated by passing a foil 170 through the algae culture in a linear pathto generate trailing vortices 330, is also ameliorated by repeatedlypassing the foil 170 through the same path to continually reinforce thevortices 330.

Vertical mixing systems known in the art may be compact, at the expenseof elevated energy consumption. In accordance with embodiments of thepresent invention, components of the vertical mixing system may bemanufactured from lightweight materials, such as plastics, which canhelp minimize capital expenditures and energy consumption for thesystem.

FIG. 42 details energy in pneumatic and hydraulic mixing systems of thepresent invention. In the exemplary embodiment, the pneumatic mixingsystem uses air and the hydraulic mixing system uses water. Consumptiondata attributable to drive element friction/fluid leakage and to driveconduit/pipe friction are specific to the motive force used in eachmixing system. Drive element friction/fluid leakage indicates energyloss due to friction between the outer surface of the drive element 190and the inner surface of the drive conduit 100, in conjunction with headloss due to fluid leaking past the drive element 190 inside the driveconduit 100. Drive conduit/pipe friction indicates energy loss due tofriction as the drive fluid flows through the pipes 410 and driveconduit 100 of the mixing system. FIG. 42 illustrates that combineddrive element friction/fluid leakage and drive conduit/pipe friction aresubstantially lower for the pneumatic mixing system than for thehydraulic mixing system.

In FIG. 42, foil assembly indicates energy consumption attributable tohydrodynamic drag on the foil assembly 180 moving through the algaeculture, which is independent of the drive system used. Comparison oftotal energy consumption and energy losses attributable to each categoryshows that a substantially higher proportion of energy is translateddirectly to moving the foil assembly 180 using the pneumatic mixingsystem than using the hydraulic mixing system.

In some embodiments, a mixing system of the present invention is used toagitate algae culture in a photobioreactor 310 intermittently. Accordingto the present invention, intermittent operation of the mixing systemprovides sufficient vertical mixing while economizing energyconsumption.

In exemplary embodiments, mixing systems of the present invention areused to agitate only portions of algae culture contained in aphotobioreactor 310. In some embodiments, horizontally oriented foils170 generate trailing vortices 330 that agitate the algae culture fromthe surface 320 to a depth that is less than the total depth of thealgae culture. The span of each foil 170 may be less than the totaldepth of the algae culture, so that the foil 170 generates trailingvortices 330 having diameters less than the depth of the algae culture113. Lateral spacing between foils 170 may be greater than the span ofeach foil 170.

In some embodiments, vertically oriented foils 170, each having a spanless than the depth of the algae culture, agitate the algae culture fromthe surface 320 to a depth that is less than the total depth of thealgae culture.

In some embodiments, the foil assembly 180 traverses only a portion ofthe length of the photobioreactor 310, agitating the algae culturecontained in that portion while leaving the algae culture in theremaining portion of the photobioreactor 310 unmixed.

Example 1

Both hydraulic and pneumatic drive fluids have been used to propel amagnetically coupled foil assembly 180 through a photobioreactor 310 at0.5 meters per second. In a preferred embodiment, the foil assembly 180traverses the 50 foot length of a commercial scale photobioreactor 310at 0.5 meters per second for a defined time interval (usually 30seconds) before the foil assembly 180 reverses direction of motion. Theminimum steady state power requirement for motion of a foil assembly 180according to these specifications has been determined by measuring fluidpressures and flow rates while the foil assembly 180 moves at a constantspeed. This determination neglects any additional energy consumption orefficiency that occurs during the few seconds when the foil assembly 180is moving at less than 0.5 meters per second while reversing directionof motion.

Using hydraulic drive fluid and a drive ferromagnet 144, measurementsindicate a pressure drop of 8 to 9 pounds per square inch perphotobioreactor 310 at a fluid flow rate of 2 gallons per minute.Without accounting for pump 420 and drive efficiency, the minimum powerrequirement using water as a drive fluid is determined by

Power_(min)=ΔPressure×Flowrate=7.8 Watts per photobioreactor310  Equation 1:

which is equivalent to 0.34 Watts/m² for a 23 m² photobioreactor 310.

Power requirements have not varied in photobioreactors 310 containingeither freshwater, seawater or algae culture. Accordingly, powerconsumption by mixing systems of the present invention used in liquidnot containing algae culture is substantially equivalent to powerconsumption by mixing systems of the present invention used in liquidcontaining algae culture. According to the present invention, drag onthe foil assembly 180 is mostly due to inertial forces, rather thanviscous forces, and the densities of all fluids tested in thephotobioreactor 310 are roughly equivalent.

A preponderance of power loss in mixing systems of the present inventionthat use hydraulic drive fluid were attributable to fluid leakage pastthe drive ferromagnet 144 and the resulting increased pressure drop toforce the hydraulic fluid, typically water, through the drive conduits100 and pipes 410. Using a pneumatic drive fluid significantly reducedpressure drop over the drive ferromagnet 144 due to the lower viscosityof gas, typically air, compared to water and other fluids and due to theuse of seals to reduce fluid leakage past the drive ferromagnet 144.Thus, mixing systems of the present invention that incorporate afloating pneumatic seal around the drive ferromagnet 144 and uselubricated aft typically have operated at 3 to 4 pounds per square inchat 5 to 6 standard liters per minute.

Four pneumatically driven mixing systems have been operated outdoorswith 6.16±6% standard liters per minute of air consumed by each(referenced at 25 degrees Celsius) under 2.75±0.05 pounds per squareinch. Using the standard equation for calculating the power required tocompress gas adiabatically, the minimum energy requirement is thus 1.82Watts/photobioreactor 310, or 0.08 Watts/m².

Net energy usage for a commercial mixing system of the present inventionto power 240 photobioreactors 310, based on distribution losses of 5%©,a compressor of 50% efficiency and an electrical drive of 90% efficiencyyields a minimum energy requirement of 4.26 Watts/photobioreactor 310,or 0.185 Watts/m². An array of 240 photobioreactors 310, as illustratedin FIG. 23, would require the use of a rotary lobe compressor rated at1.5 horsepower. A commercial plant with a centralized compressor systemmay utilize a more efficient compressor to reduce the powerrequirements. It is also possible to use bleed air from the firstcompression stages of a power generating gas turbine as the pneumaticdrive fluid, which may reduce net energy cost if the efficiency ofconversion of fuel energy to electricity is considered.

The energy required to run a pneumatically driven foil assembly 180 isroughly equivalent to that required for a large raceway system runningat 0.25 meters per second, with an 8 inch algae culture depth. The netpower requirements for both systems are approximately 0.2 Watts/m².Thus, the operating expense for both systems is $1230 per hectare peryear assuming an energy cost of $0.07 per kilowatt hour. The operatingexpense is higher for small raceway systems, however. One majormanufacturer of raceway paddlewheels (Waterwheel Factory, Inc.)estimates that motors rated for at least 20-40 Watts would be requiredto provide mixing in photobioreactors 310 measuring 5 feet by 50 feetunder the most optimistic conditions, which is a factor of 5-10 timeshigher power requirement than the exemplary foil mixed systems.

Example 2

Growth of cyanobacteria in response to mixing was compared in tworeactor types that varied in mixing system design. Two closed foil-mixedphotobioreactors and two closed flume-style raceway pondphotobioreactors were tested. The oval-shaped raceway pondphotobioreactors and the foil-mixed photobioreactors were constructedand enclosed using the same thin, flexible polymeric film.

Inoculum cultures of a unicellular cyanobacterium were scaled in50-liter flat-panel culture vessels. The inoculum cultures were thentransferred into the two raceway pond photobioreactors and the twofoil-mixed photobioreactors containing seawater and BG-11 nutrient mix.Each raceway pond photobioreactor contained approximately 460 liters ofseawater and each foil-mixed photobioreactor contained approximately 900liters of seawater. Sunlight entered each reactor across the top surfaceonly, and the culture depth in each reactor was 8 inches (20centimeters), yielding equal surface area to volume ratios for the fourreactors The seawater in each photobioreactor was pre-filtered to 0.2-μmand had salinity of 35.

Air was delivered to each photobioreactor at a rate of 5 liters perminute, and carbon dioxide was added from 08:00 to 18:00 local standardtime, controlled to a volumetric ratio of 10% carbon dioxide to air.Each photobioreactor was maintained under ambient irradiance andtemperature conditions.

The culture contained in each foil-mixed photobioreactor was mixed usinga foil assembly comprising four foils positioned at a depth of fourinches in the algae culture contained in the photobioreactor. Each foilhad a span of seven inches and a chord of four inches. The foils werespaced with their centerlines 14 inches apart.

The foil speed traversing the length of the foil-mixed photobioreactorwas maintained at 0.5 meters per second while the foil was in motion.When the foil reached each end of the photobioreactor, the motion of thefoil was paused for 20 to 22 seconds in order to simulate the period ofthe foil, and thus vortex reinforcement frequency, in a 50 foot-longcommercial-scale, foil-mixed photobioreactor.

Each raceway photobioreactor was operated similarly to a paddlewheelraceway in which horizontal motion of culture was maintained throughpumping and recirculation of the flow. Rather than using a paddlewheel,however, pumping in the raceway photobioreactors was accomplished usingfour Tunze® Turbelle® stream 6085 pumps in each bioreactor. These arepropeller pumps with a 90 mm (3.5 in.) ball design generally used forwater circulation in aquariums or tanks. Each Tunze® Turbelle® stream6085 produces flow rate of about 8 liters per hour at power consumptionof about 14 Watts, but the particular power consumption of these pumpsis of secondary importance. Rather, the horizontal flow that theyproduced in the raceway photobioreactor was the target. The pumps werearranged to provide a flow rate of 0.25 m/s in an 8 inch (20 cm) deepculture in the photobioreactor raceways. This flow rate was calculatedfollowing Weissman et al., “Photobioreactor Design: Mixing, CarbonUtilization, and Oxygen Accumulation,” Biotechnology and Bioengineering,Vol. 31, Pp. 336-344 (1988), equating the electrical energy consumptionof a commercial scale paddlewheel system to generate this flow (0.21Watts/square meter) to the power to drive the pneumatic foil system. Thepower requirement was determined using Manning's equation for hydraulicloss. Drive efficiency was estimated as 0.31 for a paddlewheel operatingat the specified speed and depth on a 100 square meter raceway. Thedrive efficiency could be as high as 0.5 for a very large system, butthe increased efficiency would not significantly increase the flow rate,i.e., to 0.28 meters per second, under the stated power consumption.Raceway reactors are also typically operated at mixing speeds of0.15-0.25 meters per second to minimize settling of algae in theculture.

As shown in Table 1, volumetric dry weight of the unicellularcyanobacterium in each algae culture was measured for eachphotobioreactor three times per week for three weeks, as each culturematured from growth phase to early stationary phase. Dry weight arealbiomass of the unicellular cyanobacterium in each algal culture, shownin Table 1, was calculated based on measured culture volumes and thesurface areas of the culture in each photobioreactor, shown in Table 2.

TABLE 1 Time Raceway PBR 1 Raceway PBR 2 Foil Mixed PBR 1 Foil Mixed PBR2 (day) mg/L g/m² mg/L g/m² mg/L g/m² mg/L g/m² 0.7 59.33 11.67 14.672.98 57.26 12.02 62.07 13.35 2.4 85.83 16.88 72.50 14.75 67.70 14.2297.22 20.90 4.4 218.52 42.98 209.63 42.66 209.63 44.02 194.81 41.89 7.3380.00 74.73 351.11 71.45 455.56 95.67 443.33 95.32 10.3 397.64 78.20435.56 88.64 513.33 107.80 475.56 102.24 11.3 379.17 74.57 369.44 75.18433.33 91.00 419.44 90.18 14.4 390.00 76.70 460.00 93.61 466.67 98.00490.00 105.35 16.3 425.00 83.58 460.00 93.61 580.00 121.80 536.67 115.3818.3 420.00 82.60 540.00 109.89 660.00 138.60 636.67 136.88 21.3 N/A N/AN/A N/A 587.73 123.42 541.67 116.46

TABLE 2 Reactor SA (m²) Volume (L) Raceway PBR 1 2.31 454 Raceway PBR 22.31 470 Foil Mixed PBR 1 4.23 889 Foil Mixed PBR 2 4.31 926

The logistic growth model stated in Equation 2 (Kot, “Elements ofMathematical Ecology” Cambridge University Press (2001)) wasparameterized from the areal data in each photobioreactor as listed inTable 1.

$\begin{matrix}{{B(t)} = \frac{{KB}_{0}^{\mu \; t}}{K + {B_{0}( {^{\mu \; t} - 1} )}}} & {{Equation}\mspace{14mu} 2}\end{matrix}$

wherein

t=time (day);

μ=specific growth rate (1/day);

B₀=initial biomass (g−DW/m²); and

K=biomass abundance at stationary phase (g−DW/m²).

Values of the parameters in Equation 2 obtained from nonlinear leastsquare fit of the logistic growth model to the data in Table 1 are shownin Table 3:

TABLE 3 Max Growth PBR μ K Rate (g/m²/d) R² Raceway PBR 1 0.6741 79.9713.4783 0.987 Raceway PBR 2 0.4740 96.14 11.3931 0.952 Foil Mixed PBR 10.4911 117.81 14.4658 0.922 Foil Mixed PBR 2 0.4307 116.90 12.5867 0.935p value 0.3921 0.069 0.519 t-stat* 1.083 −3.618 −0.777 Significant? NoYes (90%) No *2-tailed t-test

Plots of the average dry weight areal biomass data for each replicatephotobioreactor type in Table 1 and the parameterized logistic growthmodels in Equation 2 for averaged data from both reactor types areoverlain in FIG. 43. If an exponential model of growth is assumedinstead of a logistic model and specific growth, μ, is calculated asln(B₂/B₁)/(t₂−t₁), where t₁=2.4 days and t₂=7.3 days, then specificgrowth rates average 0.343±0.055 and 0.307±0.013, respectively tofoil-mixed and raceway PBRs, and are not significantly different (t-teststat=0.8969, p=0.4644).

As shown in Table 4, both measured and modeled cumulative biomass growthat day 16 are significantly greater in the foil-mixed photobioreactorsthan in the raceway photobioreactors:

TABLE 4 16-day cumulative biomass growth (g/m²) Measured Cum. ModeledCum. Growth (g/m²) Growth (g/m²) Reactor Mean Std. Dev. Mean Std. Dev.Foil Mixed PBRs 118.6 4.5 116.5 1.01 Raceway PBRs 88.6 7.1 87.5 10.7t-stat 5.0375 3.6612 p value 0.0372 0.0672 Significant? Yes (95%) Yes(90%)

Example 3

Capital expense is compared for conventional mixing technology usingpaddlewheels to mix shallow algae cultures and for a mixing system inaccordance with the present invention using a magnetically coupled,moving foil assembly. Details of the capital expense for large scalepaddlewheel systems have been published in Weissman et at Twopaddlewheel systems described therein are adapted for 0.4 hectare and 8hectare ponds. The paddlewheel mixer capital expense totals adjusted topresent day values are approximately $11,000 and $36,000 for the 0.4hectare and 8 hectare ponds, respectively. As noted in Table 5, thesecapital expense totals are equivalent to approximately $53,000 and$9,000 per hectare, respectively,

TABLE 5 5 × 50 ft reactor area (23 m²) Open Sealed Film Componentchannel Photobioreactor center barrier $116 paddlewheel $37 $37 supportguard poles $2 flange $40 $40 bearings lip seals $40 paddlewheel $22 $22shaft ⅜ SS $45 $45 end fairings $15 gear motor $40 $40 Capex/PBR $184$356 Capex/hectare $80,122 $154,966 Industrial scale raceway pondsWeissmann & Goebel 1987* Capex/hectare $52,770 (0.4 hectare)Capex/hectare $8,850 (8 hectare) *Cost adjusted for 2011

An independent estimate for the lowest cost of a paddlewheel mixingsystem suitable for use in an open 23 square meter (0.0023 hectare)raceway pond, which is equivalent to the typical size of an enclosedbioreactor measuring 5 feet by 50 feet, was determined by estimating thelowest material costs for a design provided by Waterwheel Factory, Inc.,a major waterwheel manufacturer. The estimated material costs are shownin Table 2.

At $184 per raceway photobioreactor, the capital expense per hectare fora small-scale paddlewheel mixing system is approximately $80,000 perhectare. This estimate is plotted in FIG. 44 along with historicalpublished data. As show by the dotted line plotted in FIG. 44, there isa trend toward increased capital expense per area with smaller racewaysystems.

The capital expense for a foil mixing system in accordance with thepresent invention used with a 23 square meter enclosed photobioreactoris detailed in Table 6.

TABLE 6 Compo- feet of total nent Specification piping lb/ft¹ $/ft² costheader 1.5″ SDR11 610 0.411 0.492 $300 piping (central row) header 1.25″1420 0.16 0.192 $273 piping SDR15.3 (sides) mixer ½″ SDR10.1 12,4800.048 0.0576 $719 tubing quantity $/item compressor 1.5 hp rotary 1 1000$1,000 lobe blower electronics ABB VFD or 1 350 $350 and control 4-wayvalve external NdFeB Grade 240 6.4 $1,536 magnets N42 1.25″ OD X 0.75″ID X ⅛″ internal NdFeB Grade 480 2.37 $1,138 magnets N40 0.5″ OD X 0.25″ID X ¼″ mixer³ 2 lbs HDPE 240 4.38 $1,051 cost/ $6,366 module⁴ cost/PBR⁵$27 cost/ $11,533 hectare ¹Performance Pipe IPS size data for PE 4710.²$1.20/lb in accord with pricing from Ferguson Enterpries, Inc. ³Costcalculated by 3× cost of plastic for standard blow molding, $0.73/lb inaccord with ICIS pricing. ⁴1 module consists of 240 photobioreactorsarranged as in FIG. 23. ⁵Each photobioreactor is 5 feet wide by 50 feetlong and has a wet area of 23 square meters.

The capital expense illustrated in Table 6 includes the drive anddistribution components of the pneumatic drive foil mixing system for aset of 240 photobioreactors (in 4 rows of 60). Here, the capital expenseper bioreactor is $27, or approximately $11,500 per hectare. Thus, thecapital expense per area for a facility constructed usingphotobioreactor modules of this size is independent of the size of thefacility.

Capital expense is compared for foil mixing systems and raceway mixingsystems in Table 7 and FIG. 44.

TABLE 7 individual reactor size (hectare) Capex/hectare open paddlewheel8 8,848 Weissman&Goebel (1987) open paddlewheel 0.4 52,772Weissman&Goebel (1987) open channel 0.0023 80,122 paddlewheel estimatesealed film PBR 0.0023 154,966 paddlewheel estimate foil mixer 0.002311,533

The data in Table 7 and FIG. 44 show that the currently sized foilmixing system is approximately one order of magnitude less expensivethan raceway paddlewheel mixing systems on an areal basis, except forraceways which approach a size of 8 hectares. Thus, foil mixing reducesthe capital cost of mixing on all scales which can be enclosed atreasonable expense. Even if the cost to enclose a 0.4 hectare(approximately 1 acre) pond was negligible, foil mixing systems arestill 4.5 times less expensive than raceway paddlewheel mixing systems.The cost for a sealed raceway system would exceed the estimates shown inTable 6 due to the cost of seals, guards, central barriers and endpieces that would need to be manufactured for the photobioreactors.

The foregoing Examples 1 through 3 demonstrate that the biomass outputof a foil mixed system was comparable or better than a raceway pond,while the operating expense of the foil system was equivalent or lower.The most distinctive advantage of the foil mixed system is its lowcapital expense, which makes up a large fraction of the total cost evenwhen spread over a 15 year operating period as shown in Table 8. Capitalexpense is a much larger fraction of the total expense for thepaddlewheel raceway systems for areas that are practical to enclose(e.g. 23 square meters). Thus the total cost of mixing to generatebiomass is much higher in the paddlewheel system, by a factor as largeas 8. Here the cost of mixing is only about 4 cents per kilogram of dryweight, while cost of mixing for an enclosed paddlewheel system could be34 cents per kilogram.

TABLE 8 Pneumatically Enclosed Annual driven foil mixed paddlewheelexpenditure/hectare reactors (23 sq. m) reactors (23 sq. m) Capex/15years¹ 769 10,331 Opex 1,230 ⁽²⁾5,775  Total 1,999 16,106 Biomass yieldper year³ 47,450 47,450 Total cost⁴ ($/kg of 0.042      0.339 biomass)¹Interest on loan not considered in either case. ²20 Watts perphatobioreactor as the minimum suggested by Waterwheel Factory, Inc. for0.25 meters per second flow. ³Assuming maximum growth rate (13 grams persquare meter per day) demonstrated in Example 2 is sustained over ayear. ⁴Considering only the cost of mixing.

In certain embodiments, as illustrated in FIGS. 46, 47 and 48, the depthof the algae culture is shallow and a crossbar 590 is used to create ashallow breaking wave front 600 on the surface 320 of the algae culture.In certain embodiments, the depth of the algae culture is preferablyapproximately 1 to 2 inches. In certain embodiments, the depth of thealgae culture is preferably approximately 1 inch. The crossbar 590 isattached to a follower element 110 that is disposed on a drive conduit100. The crossbar 590 is propelled using magnetic coupling between thefollower element 110 and a drive element 190, to which pneumatic orhydraulic motive force is applied.

The crossbar 590 is propelled at sufficient speed to displace fluidalong the length of the photobioreactor 310, such that a wave front 600is generated that moves at a higher speed than the shallow water wave inthe direction of travel of the crossbar 590. For an algae culture of 1inch depth, a wave front 600 may be generated by a crossbar traveling at0.5 meters per second.

The wave front 600 generated at the surface 320 of the algae cultureprovides enhanced mass transfer between the liquid algae culture and theair above the surface 320 of the algae culture. Dissolved oxygen contentin the algae culture would be lower when a breaking wave front 600 isgenerated than when a breaking wave front 600 is not generated in thealgae culture. The wave front 600 also generates provides verticalmixing of the algae within the culture, which enhances photosyntheticproductivity and diffusion of nutrients.

The range of traverse, or stroke length, of the crossbar 590 may besubstantially shorter than the length of the photobioreactor 310. Strokelength can be controlled by placing stoppers inside the drive conduit100 to restrict the motion of the drive element 190 or around theoutside of the drive conduit 100 to restrict the motion of the followerelement 110. In one embodiment, a stroke length of 1 meter is sufficientto generate a wave front 600 that can propagate for 80% of the length ofthe photobioreactor 310. Shorter stroke length of the wave front 600produces shorter propagation distance of the wave front 600.

A wave front 600 can be created in a photobioreactor 310 that is 50 feetlong using 8.5-9.5 pounds per square inch hydraulic motive force in adrive conduit 100 of 0.52 inches inside diameter, which propels thecrossbar 590 at 0.33-0.5 meters per second. If the crossbar 590 islocated in the center of the photobioreactor 310, a cycle time ofapproximately 10 seconds for the crossbar 590 to complete oneoscillation allows for one breaking wave front 600 to be present oneither side of the crossbar 590 at any time, while maintaining lowenergy usage, approximately 4 Watts per photobioreactor 310, equivalentto a mixing system using a foil assembly 180.

The crossbar 590 used to generate a wave front 600 may be buoyant andmay have chamfered edges on the lower surfaces of the crossbar 590 togenerate lift, which prevents the crossbar 590 from touching the bottomof the photobioreactor 310 and reduces friction and wear on thecomponents of the crossbar 590 and the photobioreactor 310. The crossbar590 will be optimally designed such that reflections of the wave front600 are minimized. The wave front 600 preferably dissipates when itreaches the end of the photobioreactor 310 and does not disrupt themotion of the crossbar 590. Resonant operation of the crossbar 590 ispossible but may be difficult to control at low capital expense.

Multiple crossbars 590 in one photobioreactor 310 can be driven in thesame manner as a system using multiple foil assemblies 180. Incombination with reducing the stroke length of each crossbar 590, aconfiguration employing multiple crossbars 590 can be used to generatewave fronts 600 at higher frequencies, so that more than two breakingwave fronts 600 would be present in the photobioreactor 310 at any time.

Although the present invention has been described in considerable detailwith reference to certain embodiments thereof, other embodiments arepossible. Therefore, the spirit and scope of the appended claims shouldnot be limited to the description of the embodiments contained therein.

What is claimed is:
 1. A system for the production of a target moleculeor accumulation of biomass comprising: a suspension of cells in aliquid, wherein the cells are capable of producing a target molecule oraccumulating biomass; and a foil moving by magnetic means in a lineardirection in the liquid and producing vertical mixing of the suspension;wherein production of the target molecule or accumulation of biomass isgreater in the presence of the moving foil than in the absence of themoving foil; and wherein the system is a bioreactor.
 2. The system ofclaim 1, wherein the target molecule is ethanol.
 3. The system of claim1, wherein the suspension of cells comprises cyanobacteria.
 4. Thesystem of claim 1, wherein the magnetic means comprises a drive elementmagnetically coupled with a follower element attached to the foil andhydraulic or pneumatic motive force applied to the drive element,wherein the hydraulic or pneumatic motive force is transferred from thedrive element to the follower element and the foil through the magneticcoupling.
 5. The system of claim 1, wherein the linear direction ishorizontal and parallel to a top surface of the liquid.
 6. The system ofclaim 1, wherein the suspension of cells has a vertical depth defined bythe bioreactor and the foil mixes only a portion of the depth of thesuspension of cells.
 7. The system of claim 1, wherein accumulation ofbiomass is at least about 30% greater using the foil to produce verticalmixing than using a paddlewheel mixer.
 8. A system for the production ofa target molecule or accumulation of biomass comprising: a suspension ofcells in a liquid, wherein the cells are capable of producing a targetmolecule or accumulating biomass; and a foil moving by magnetic means ina linear direction in the liquid and producing vertical mixing of thesuspension; wherein the total cost of mixing per unit weight of thetarget molecule or biomass produced is lower using the foil to inducevertical mixing than using a paddlewheel mixer; and wherein the systemis a bioreactor.
 9. The system of claim 8, wherein the target moleculeis ethanol.
 10. The system of claim 8, wherein the suspension of cellscomprises cyanobacteria.
 11. The system of claim 8, wherein the magneticmeans comprises a drive element magnetically coupled with a followerelement attached to the foil and hydraulic or pneumatic motive forceapplied to the drive element, wherein the hydraulic or pneumatic motiveforce is transferred from the drive element to the follower element andthe foil through the magnetic coupling.
 12. The system of claim 8,wherein the linear direction is horizontal and parallel to a top surfaceof the liquid.
 13. The system of claim 8, wherein the suspension ofcells has a vertical depth defined by the bioreactor and the foil mixesonly a portion of the depth of the suspension of cells.
 14. The systemof claim 8, wherein the total cost of mixing per unit weight of thetarget molecule or biomass produced is at least about 80% lower usingthe foil to induce vertical mixing than using a paddlewheel mixer.
 15. Amagnetically coupled mixing system comprising: a mixing vessel; a liquiddisposed within the mixing vessel; a gas disposed within the mixingvessel; a drive conduit; a drive element disposed within the driveconduit and adapted to move in a longitudinal direction within the driveconduit; a follower member having a first distal end and a second distalend, wherein the follower member is disposed around the perimeter of atleast a portion of the drive conduit and is adapted to movelongitudinally along the drive conduit; a magnetic follower elementdisposed within the follower member, wherein the magnetic followerelement is adapted to couple magnetically with the drive element and isproximally disposed outside the drive conduit; and a crossbar having asurface shaped or configured to generate a breaking wave front inliquid, wherein the crossbar is at least partially disposed in theliquid, the breaking wave front is generated by movement of the crossbaralong a linear path in the mixing vessel, the crossbar is attached tothe follower member, and the crossbar mixes the liquid, the gas, or aninterface between the liquid and the gas.